login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A141227 Maximum number of points visible from some point in a cubic n x n x n lattice. 1

%I

%S 1,8,27,57,111,183,303,435,633,843,1155,1443,1893,2313,2895,3447,4215,

%T 4875,5865,6723,7887,8943,10371,11553,13293,14745,16707,18411,20703,

%U 22485,25257,27459,30423,32931,36291,38889,42837,45950,50115,53523

%N Maximum number of points visible from some point in a cubic n x n x n lattice.

%C Two points (a,b,c) and (d,e,f) are visible to each other when gcd(d-a,e-b,f-c)=1. Sequence A141228 gives the number of lattice points that have maximal visibility.

%H Eric Weisstein, <a href="http://mathworld.wolfram.com/VisiblePoint.html">MathWorld: Visible Point</a>

%F The maximum number of visible points is slightly more than c*n^3, with c = 1/zeta(3) = 0.831907... (A088453).

%t Table[mx=0; Do[cnt=0; Do[If[GCD[d-a,e-b,f-c]<2, cnt++ ], {a,n}, {b,n}, {c,n}]; If[cnt>mx, mx=cnt], {d,n}, {e,n}, {f,n}]; mx, {n,10}]

%Y Cf. A141224.

%K nonn

%O 1,2

%A _T. D. Noe_, Jun 15 2008

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 17 03:06 EST 2019. Contains 329216 sequences. (Running on oeis4.)